Microelectromechanical system (“MEMS”) resonators are small electromechanical structures that vibrate at high frequencies and are often used for timing references, signal filtering, mass sensing, biological sensing, motion sensing, and other applications. MEMS resonators are considered a common alternative to quartz timing devices to provide an accurate time or frequency reference. In general, quartz resonators have a high quality factor and piezoelectric coupling. High quality factor indicates a low rate of energy loss relative to the stored energy of the resonator, i.e., the oscillations die out more slowly. However, one limitation for quartz resonators is that they are difficult to design in smaller sizes.
Accordingly, MEMS resonators have been used as an alternative for devices and applications that are required to be smaller than available quartz resonators. Moreover, to maximize the quality factor, such MEMS resonators have been designed to resonate in a bulk mode where the resonator deforms mainly in the in-plane where the out-of-plane movement is minimized. In particular, it is desirable that out-of-plane bending modes of the resonator are avoided as these modes have low quality factors at high frequencies.
Furthermore, the resonance frequency of MEMS resonators is inversely related to the resonator width. Thus, to increase the resonant frequency of the resonator, device designs must reduce the width and length of the resonator accordingly. However, reducing the size of such resonators also results in higher electrical impedance, which is undesirable.
Some existing resonator designs have attempted to decrease the electrical impedance by providing an array of multiple resonators in parallel. For example, Non-Patent Document 1, identified below, demonstrates an array of coupled 10.7 MHz square plate resonators where the plates vibrate out-of-plane and are actuated with electrostatic transducers.
FIG. 1 illustrates a conventional micromechanical resonator array similar to the design disclosed in Non-Patent Document 1. As shown in FIG. 1, the resonator array 1 includes a plurality of resonator plates 10A that are respectively coupled by coupling beams 20A and 20B. However, for this design, due to electrostatic actuation and out-of-plane bending mode, the resonator array 1 is not satisfactory for frequencies higher than 20 MHz as the motional impedance would still be unacceptably high for most device implementations.
Furthermore, Non-Patent Document 2, identified below, discloses another conventional design that introduces an electrostatically actuated resonator array where the resonators are connected with a connection beam. The design disclosed in Non-Patent Document 2 also includes technical limitations as electrostatic actuation makes the motional impedance unacceptably high. Moreover, vibration of the coupling beams leads to many spurious resonances in the resonance response.
To minimize some of the limitations of the designs described above, many MEMS resonators will typically be made of silicon using lithography based manufacturing processes and wafer level processing techniques. However, because bare silicon is not piezoelectric and pure silicon resonators have high motional impedance, it has been found that adding a piezoelectric material, such as a layer of thin film of aluminum nitride (AlN), on top of the resonator yields a resonator with lower motional impedance. A typical piezoelectric MEMS resonator is shown in FIGS. 2A and 2B.
In particular, FIG. 2A illustrates a top view of a conventional width extensional resonator 10. As shown, resonator 10 is rectangular shaped (although other shapes have been used) with a lateral length L and width W. Moreover, resonator 10 includes two smalls anchor 11A and 11B on the sides of the resonator to mount the resonator.
FIG. 2B illustrates a cross sectional view of the conventional resonator 10. Typically, the resonator 10 is manufactured of silicon using MEMS manufacturing techniques. On top of silicon substrate 12, the resonator 10 has a piezoelectric thin film 16 sandwiched between two metal electrodes 14A and 14B to provide piezoelectric coupling. In an exemplary design, the metal electrodes 14A and 14B are typically molybdenum, but other materials such as platinum or aluminum may also be used. Moreover, the piezoelectric film 16 may be aluminum nitride (AlN) or doped aluminum nitride, but may also be PZT or titanium oxide.
As noted above, to maximize the quality factor of resonator 10, it is desirable that the resonator resonates in a bulk mode where the resonator deforms mainly in in-plane and the out-of-plane movement is minimized. In particular, it is desirable that out-of-plane bending modes of the resonator are avoided as these modes have low quality factors at high frequencies. Moreover, for the bulk vibration modes, the lateral resonator dimensions determine the resonator resonance frequency and are important in designing high quality factor resonators. A good design with a high quality factor has a rectangular shape with width W and length L as shown in FIG. 2A. The motion of the resonator 10 is mainly in the width direction and the resonator is referred to as the width-extensional resonator.
FIG. 2C illustrates a top view of the width extensional resonator 10 according to a conventional design in which the vibrational motion of the resonator 10 is mainly in the width direction (i.e., contraction and expansion vibration). This mode is preferred as the anchoring points 11A and 11B on the short side of the resonator have minimal movement, and, therefore, minimize the anchor losses and maximize the quality factor.
Referring back to FIG. 2A, it is also known that certain aspect ratios (“AR”), defined as the ratio of length L to width W (i.e., AR=L/W), minimize the mounting losses and therefore maximize the quality factor, for example, as described in Patent Document 1, identified below. In particular, an optimal aspect ratio ranges from 1.2 to 1.8 depending on material properties and is typically around 1.5 for silicon based resonators.
As further noted above, the resonance frequency is inversely related to the resonator width. However, small resonators with increased resonant frequencies also experience higher electrical impedance that is undesirable. Accordingly, some existing resonator designs combine multiple resonators in an array to lower the electrical impedance. For example, Patent Document 2, identified below, describes an in-plane mode resonator array where resonators are actuated with a piezoelectric transduced element that is arranged laterally between at least two resonator elements. However, the design disclosed in Patent Document 2 also experiences technical limitation in that by arranging the coupling to be laterally between the elements, additional vibrating elements are introduced that may disturb the resonator mode shape, resulting in an unsatisfactory frequency response.
Patent Document 1: U.S. Pat. No. 5,548,180.
Patent Document 2: U.S. Pat. No. 8,786,166.
Non-Patent Document 1: Clark et al., “Parallel-Coupled Square-Resonator Micromechanical Filter Arrays”, IEEE International Frequency Control Symposium and Exposition, pp. 485-490 (2006).
Non-Patent Document 2: Bhave et al., “Fully-Differential Poly-SiC Lame Mode Resonator and Checkerboard Filter”, 18th IEEE International Conference on Micro Electro Mechanical Systems, pp. 223-226 (2005).